irreducible

[ ir-i-doo-suh-buhl, -dyoo- ]

adjective

1. not reducible; incapable of being reduced or of being diminished or simplified further:

   the irreducible minimum.

2. incapable of being brought into a different condition or form.
3. Mathematics.
   1. of or relating to a polynomial that cannot be factored.
   2. of or relating to a group that cannot be written as the direct product of two of its subgroups.

irreducible

/ ˌɪrɪˈdjuːsɪbəl /

adjective

1. not able to be reduced or lessened
2. not able to be brought to a simpler or reduced form
3. maths
   1. (of a polynomial) unable to be factorized into polynomials of lower degree, as ( x ² + 1)
   2. (of a radical) incapable of being reduced to a rational expression, as √( x + 1)

Derived Forms

• ˌirreˈducibly, adverb
• ˌirreˌduciˈbility, noun

Other Words From

• irre·duci·bili·ty irre·duci·ble·ness noun
• irre·duci·bly adverb

Word History and Origins

Origin of irreducible¹

First recorded in 1625–35; ir- ² + reducible

Example Sentences

Climate and weather patterns are driven by an irreducible web of interactions across a variety of planet-wide systems.

From Singularity Hub 

First, the United States and China must have a clear, granular understanding of each other’s irreducible strategic redlines in order to help prevent conflict through miscalculation.

From Time

Branching out to consider the moral crises of the pastor’s wife and children, the novel presents an electrifying examination of the irreducible complexities of an ethical life.

From Washington Post

The qualia that compose conscious experiences are irreducible, incapable of being mapped onto anything else.

From Nautilus

But breakfast was practically over, and the need for beating a further retreat was thus reduced to an irreducible minimum.

From Project Gutenberg

You know, to men like your father convictions are irreducible elements—they can't be split up, and differently combined.

From Project Gutenberg

There was one peculiarly stubborn and irreducible class of facts which he took up and gave much thought to during this period.

From Project Gutenberg

The logic is unimpeachable, and points to irreducible pleasures and pains as the standard of valuation.

From Project Gutenberg

What wonder, then, if he should sometimes make mistakes, and that some inconsistencies remain at last irreducible?

From Project Gutenberg